Abstract

We consider the pricing of exotic options when the price dynamics of the underlying
risky asset are governed
by a discrete-time Markovian regime-switching process driven by an observable, high-order
Markov model (HOMM). We assume that the market interest rate, the drift, and the volatility
of the underlying risky asset's return switch over time according to the states of the
HOMM, which are interpreted as the states of an economy. We will then employ the well-known
tool in actuarial science, namely, the Esscher transform to determine an equivalent martingale
measure for option valuation. Moreover, we will also investigate the impact of the high-order
effect of the states of the economy on the prices of some path-dependent exotic options, such
as Asian options, lookback options, and barrier options.

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